You can start and stop the ride to pause it (what I do), or use auto-pause. If you have a power meter you should turn auto-pause off, otherwise it doesn't matter, and works pretty well.

Are you using the barometer or GPS for elevation? (Do you even have a choice on Edges?)

Did it get wet? Run it under the sink, get caught in a rain, anything like that? It uses air pressure to sense elevation, there's a small hole in the device to let the air in. Sometimes it can get plugged up. I've run mine under the sink (hey, I get sweaty, it drips) and my Edge gets really confused because of the water pushing up into the barometer.

If not, it's a glitch, and they all get confused sometimes.